Ok here's the trig if you want it. You'll need it if you want to mathmatically calculate the size of each cut so you don't have any dutchmans or have to make any special cuts. Sorry it's so wordy, but if you follow it carefully with pencil & paper, you'll be able to do it for any size tile or
circle, plus you'll have a head start on basic trig.
The basic idea is that you have a
circle of a known radius (120inches) so you can easily find the circumference (2*pi*r = 753.9822369"), and therefore the outer tile size (753.9822369/124tile=6.08050191")but the problem is that it's a curved measurment & we don't have any curved rulers to measure the tile with.
So if you put the tile where it goes up against the outside of the 20'
circle, the square tile touches on just 2 points. The arc of of the
circle between those 2 points is a little longer, it's that 6.08050191" that we just found. Since we can't curve a flexible tape perfectly into the shape of our cut, we have to find the straight line measurement that matches it, which is the straight top of our tile.
To find the straight line top, first grab a sheet of paper & draw a huge
circle. Mark the centerpoint M. Mark 2 points at the top on the edge of the
circle about 3" apart, mark them X and Y. These represent the outer corners of the tile that touch the
circle. Now draw a straight line from X to M and Y to M. These are both radii of the
circle (120") and follow the same line as the 2 angled sides of our tile.
So now we have a pie shaped triangle inside the
circle. At the top of the
circle are 2 lines, one is the arc XY(6.08050191" long) and one is the straight line xy. We need to find the straight line XY, this is what we'll use to measure our tile.
Find the midpoint of XY and mark it T. Draw a line from T to M. Now you've split your big triangle into 2 right triangles (right triang contains one 90deg angle).
Look at triangle MTY. We know the length of one side (MY is 120"), we know it's a right triangle, & we can get one angle (angle tmy). That's enough to find the length of TY using trig. So lets get that angle tmy first:
We know an overall
circle is made up of 360 degrees. And we know our tile (incl grout) will be 124th of the overall
circle. So 360degrees/124sections=2.9032258 degrees for angle xmy. xmy is represents the angle of one full tile. But we really need just angle tmy, which is exactly half of xmy, or 1.4516129 degrees.
Now the trig. Any right triangle will have a hypot****e (long side), an adjacent side (the side that is closest to whichever of the smaller angles you're looking at, and an opposite side (farthest away from your angle). We know the angle tmy (1.4516129 deg) and the hypot****e MY (120). The basic formula is that the sine of an acute angle (in a right triangle) times the length of the hypot****e equals the length of the opposite side.:
sin(tmy) x length of MY = length of TY
sin(1.4516129) x 120 = TY
.025332714 x 120 = TY
Therefore the length of TY is 3.0399257. TY is half of XY, so XY = 6.0798514, which is the straight line measument of the top of the tile (incl 1 grout line) that corresponds to the curved measurement of 6.08050191 between the same points.
I've intentionally done it the way Kurt first did the math, with the 1/8" included in the straight measurement because it's so much easier & the error factor is almost nothing. I need a case of beer or a chocolate cake to show you how to switch that.
I know it sounds elaborate, but once you've got it down, it only takes a minute or two on a good calculator to get your segment sizes. It's worth learning so you can use it with any type of curve, incl floor designs like this , curved vcap counters, etc.
Don't know why the forum editor won't let me type hypot****e, it must think I'm using a cuss word.
